The concept of symmetric Boolean functions treated in cryptology is transplanted into quantitative logic

and the concepts of symmetric logic formulas and pseudo-symmetric logic formulas are introduced.It is pointed out that logic formulas in two valued logic are closely related to Boolean functions while they have crucial differences.It is proved that the ratio of the number of symmetric formulas with n atoms over the number of all formulas with

n

atoms converges to zero when n tends to infinite.It is proved that the set of truth degrees of symmetric logic formulas is dense in .It is proved from the viewpoint of topology that the set consisting of all symmetric logic formulas is a nowhere dense set in the classical logic metric space.